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The Resultant on Compact Riemann Surfaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, no 1, 313-358 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a notion of the resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.

Place, publisher, year, edition, pages
2009. Vol. 286, no 1, 313-358 p.
Keyword [en]
dirichlet boundary-problem, 2-dimensional l-problem, toeplitz matrices, differential-operators, quadrature identities, integrable structure, asymptotic-behavior, extremal solutions, domains, determinants
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-18099DOI: 10.1007/s00220-008-0622-2ISI: 000262411000012Scopus ID: 2-s2.0-58149513449OAI: oai:DiVA.org:kth-18099DiVA: diva2:336145
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1007/s00220-008-0622-2

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Gustafsson, Björn

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